Deep Learning for Unsupervised 3D Shape Representation with Superquadrics

The representation of three-dimensional (3D) shapes from point clouds remains a fundamental challenge in computer vision. A common approach decomposes 3D objects into interpretable geometric primitives, enabling compact, structured, and efficient representations. Building upon prior frameworks, this study introduces an enhanced unsupervised deep learning approach for 3D shape representation using superquadrics. The proposed framework fits a set of superquadric primitives to 3D objects through a fully integrated, differentiable pipeline that enables efficient optimization and parameter learning, directly extracting geometric structure from 3D point clouds without requiring ground-truth segmentation labels. This work introduces three key advancements that substantially improve representation quality, interpretability, and evaluation rigor: (1) a uniform sampling strategy that enhances training stability compared with random sampling used in earlier models; (2) an overlapping loss that penalizes intersections between primitives, reducing redundancy and improving reconstruction coherence; and (3) a novel evaluation framework comprising \emph{Primitive Accuracy}, \emph{Structural Accuracy}, and \emph{Overlapping Percentage} metrics. This new metric design transitions from point-based to structure-aware assessment, enabling fairer and more interpretable comparison across primitive-based models. Comprehensive evaluations on benchmark 3D shape datasets demonstrate that the proposed modifications yield coherent, compact, and semantically consistent shape representations, establishing a robust foundation for interpretable and quantitative evaluation in primitive-based 3D reconstruction.